The sum of an arithmetic series where t1 = -2, t3 = 7, and n = 15 is

Answer:

Below in bold.

Step-by-step explanation:

f(x) = 1/2x^2 + 4x

Convert to vertex form:

f(x) = 1/2(x^2 + 8x)

= 1/2 [(x + 4)^2 - 16]

= 1/2(x + 4)^2 - 8    <------ Vertex form.

So the Vertex is at (-4, - 8).

Axis of symmetry is x = -4.

y -intercept (when x = 0) =  8-8 = 0.

Answer:

see explanation

Step-by-step explanation:

given a quadratic function in standard form

f(x) = ax² + bx + c ( a ≠ 0 ) , then

the x- coordinate of the vertex is

[tex]x_{vertex}[/tex] = - [tex]\frac{b}{2a}[/tex]

f(x) = [tex]\frac{1}{2}[/tex] x² + 4x ← is in standard form

with a = [tex]\frac{1}{2}[/tex] , b = 4 , c = 0 , then

[tex]x_{vertex}[/tex] = - [tex]\frac{4}{1}[/tex] = - 4

substitute x = - 4 into f(x) for corresponding y- coordinate of vertex

f(- 4) = [tex]\frac{1}{2}[/tex] (- 4)² + 4(- 4) = [tex]\frac{1}{2}[/tex] × 16 - 16 = 8 - 16 = - 8

vertex = (- 4, - 8 )

the equation of the axis of symmetry is a vertical line passing through the vertex with equation

x = c ( c is the x- coordinate of the vertex ) , then equation of axis of symmetry is

x = - 4

to find the y- intercept substitute x = 0 into f(x)

f(0) = [tex]\frac{1}{2}[/tex] (0)² + 4(0) = 0 + 0 = 0

then y- intercept is 0

Answer:

I think the answer is 43.8

Answer:

198.4

Step-by-step explanation:

Right side is a rectangle   12.8 * 12.8 = 163.84 cm^2

Left side is triangle   area = 1/2 Base * height = 1/2 * 12.8 * (18.2-12.8) =

         34.56 cm^2

summed = 198.4  cm^2

Answer:

20%

Step-by-step explanation:

8 -> pizzas

12 -> hamburgers

14 -> pastas

6 -> steaks

40 = 8 + 12 + 14 + 6 -> total dishes

so the probability become from actual cases on total cases

so (8 / 40)

8/40 = 1/5 = 20/100 = 20%

Answer:

240 cm

Step-by-step explanation:

18*12= 216

+

4*3*2= 24

216*24= 240

Answer:

$1890.57

Step-by-step explanation:

First we put the 70% on the original 1011, we can do this by multiplying 1011 by 1.7, now we have 1718.7

Now we put on the 10% tax on the new price, we can do this by multiplying 1718.7 by 1.1, now we get 1890.57

Therefore, the final retail price of the mower is $1890.57, respectively

Answer:

expand the equation

then make q the subject of the formal

Answer:

-35, 1493

Step-by-step explanation:

p(x) = 2x⁴ + 3x³ - 9x² + 16x + 13

p(-3) = 2(-3⁴) + 3(-3³) - 9(-3²) + 16(-3) + 13

-3² = 9

-3³ = -27

-3⁴ = 81

p(-3) = 2(81) + 3(-27) -9(9) - 48 + 13

p(-3) = 162 - 81 - 81 -48 + 13

81 + 81 = 162 therefore 162 - 81 - 81 cancels

-48 + 13 = -35

p(5) = 2(5⁴) + 3(5³) - 9(5²) + 16(5) + 13

5² = 25

5³ = 125

5⁴ = 625

p(5) = 2(625) + 3(125) - 9(25) + 80 + 13

p(5) = 1250 + 375 - 225 + 93

p(5) = 1250 + 150 + 93

p(5) = 1493

Answer:

c

Step-by-step explanation:

The distance the brake anchor has to be placed away from the base of the ending tree so the just reach the tree is 40.31 feet.

From the information given, the height of the tree is given as 20ft. The brake anchor 35 feet from the base of the ending tree.

Therefore, the distance the brake anchor has to be placed away from the base of the ending tree so the just reach the tree will be:

d² = ✓20² + ✓35²

d² = ✓400 + 1225

d² = ✓1625

d = 40.31 feet.

Learn more about distance on:

https://brainly.com/question/17273444

#SPJ1

The number of rows of beans that are in the garden is 24 rows.

The first step is to convert feet to inches.

1 feet = 12 inches

30 x 12 = 360 inches

The second step is to divide 360 inches by 15 inches: 360 / 15 = 24 rows

To learn more about division, please check: https://brainly.com/question/194007

#SPJ2

Answer:24

Step-by-step explanation:

Answer:

24

Step-by-step explanation:

you have to add them

Work Shown:

Range = Max - Min

Range = Oldest - Youngest

Range = 35 - 6

Range = 29

The range of 29 is the gap between the youngest person and the oldest.

Answer:

x=55 degrees

Step-by-step explanation:

Because triangle is 180 degrees,

35+90+y=180

y=55

Answer:

x = 55 degrees

Step-by-step explanation:

The angles in a triangle add up to 180 degrees. We are already given 2/3 of the angles that make up the triangle.

The two given angles are 35 degrees and 90 degrees (we got the ninty from the right angle)

We can add these given angles together and subtract them by 180 to find the measure of the missing angle:

35 + 90 = 125

180 - 125 = 55 degrees

Answer:

V =704 m^3

Step-by-step explanation:

Remark

The Volume of a cubical Prism = Length * Width * Height of L * w * h

Givens

L = 22 meters

w = 4  meters

h = 8 meters

Solution

V = L * w * h

V = 22 * 4 * 8

V = 704 m^3

What is the volume, in cubic meters, of a rectangular prism that has a length of 22 meters, a width of 4 meters, and a height of 8 meters?

In this question we are provided with the length, breadth and height of a rectangular prism. We are asked to calculate the volume of the rectangular prism.

We know,

[tex] \star \: \small\boxed{ \rm{ Volume_{(rectangular \: prism)} = L×B×H}}[/tex]

Where,

Substituting the values we get

[tex] \small\sf{ Volume_{(rectangular \: prism)} = 22×4×8 = 704 m³}[/tex]

Hence, the volume of the rectangular prism is 704 m³.

Check the picture below.

[tex]\cos(28^o)=\cfrac{h}{5}\implies 5\cos(28^o)=h \\\\[-0.35em] ~\dotfill\\\\ \textit{area of a parallelogram}\\\\ A=bh~~ \begin{cases} b=base\\ h=height\\[-0.5em] \hrulefill\\ b=6\\ h=5\cos(28^o) \end{cases}\implies A=6[5\cos(28^o)]\implies A\approx 26.49[/tex]

Make sure your calculator is in Degree mode.

Problem 9

a = 500 = initial amount

b = 1+r/n = 1 + 0.034/52 = 1.000654 = approximate growth factor

The equation goes from [tex]y = a*b^x[/tex] to [tex]y = 500*1.000654^x[/tex] where x is the number of weeks and y is the account balance in dollars.

Plug in y = 700 and isolate x by using logarithms.

[tex]y = a*b^x\\\\y = 500*1.000654^x\\\\700 = 500*1.000654^x\\\\700/500 = 1.000654^x\\\\1.4 = 1.000654^x\\\\1.000654^x = 1.4\\\\\log(1.000654^x) = \log(1.4)\\\\x\log(1.000654) = \log(1.4)\\\\x = \log(1.4)/\log(1.000654)\\\\x = 514.652\\\\x = 515\\\\[/tex]

It takes about 515 weeks for the account balance to reach $700

This is equivalent to roughly 515/52 = 9.904 years

===========================================================

Problem 10

The formula to calculate the monthly payment is not a simple exponential growth or decay function. I'm not sure how your teacher wanted you to answer this question. You'll have to get clarification on it.

If your teacher is asking something along the lines of "$240,000 is invested at a rate of 1.2% compounded bimonthly. How many years does it take to have the investment reach $300,000?" then you could follow these steps below.

a = 240,000 = initial amount

b = 1 + r/n = 1 + 0.012/24 = 1.0005 = growth factor

[tex]y = a*b^x\\\\y = 240000*1.0005^x\\\\300000 = 240000*1.0005^x\\\\240000*1.0005^x = 300000\\\\1.0005^x = 300000/240000\\\\[/tex]

[tex]1.0005^x = 1.25\\\\\log(1.0005^x) = \log(1.25)\\\\x\log(1.0005) = \log(1.25)\\\\x = \log(1.25)/\log(1.0005)\\\\x = 446.3987\\\\x = 446\\\\[/tex]

The x represents the number of bimonthly periods. There are 24 bimonthly periods in a year, which means it takes roughly 446/24 = 18.58 years for the starting balance of $240,000 to reach $300,000.

Keep in mind that the steps above are based on the assumption I made at the top of the problem. If that assumption is incorrect, then ignore the steps and answer entirely.

#9

[tex]\\ \rm\Rrightarrow P=P_o(1+r/n)^t[/tex]

we need t

[tex]\\ \rm\Rrightarrow P=500(1+0.034/52)^t[/tex]

[tex]\\ \rm\Rrightarrow 700=500(1+0.000654)^t[/tex]

[tex]\\ \rm\Rrightarrow 700=500(1.000654)^t[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{7}{5}=(1.000654)^t[/tex]

[tex]\\ \rm\Rrightarrow 1.4=1.000654^t[/tex]

[tex]\\ \rm\Rrightarrow log1.4=log1.000654^t[/tex]

[tex]\\ \rm\Rrightarrow log1.4=tlog1.000654[/tex]

[tex]\\ \rm\Rrightarrow t=\dfrac{log1.4}{1.000654}[/tex]

[tex]\\ \rm\Rrightarrow t\approx 514.6\approx 515weeks[/tex]

#2

[tex]\\ \rm\Rrightarrow P=240000(1+0.012/25)^t[/tex]

[tex]\\ \rm\Rrightarrow 300000=240000(1.0005)^t[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{5}{4}=(1.0005)^t[/tex]

[tex]\\ \rm\Rrightarrow 1.25=(1.0005)^t[/tex]

[tex]\\ \rm\Rrightarrow log1.25=log1.0005^t[/tex]

[tex]\\ \rm\Rrightarrow log1.25=tlog1.0005[/tex]

[tex]\\ \rm\Rrightarrow t=\dfrac{log1.25}{1.0005}[/tex]

[tex]\\ \rm\Rrightarrow t=446.4\approx 446[/tex]

Question is bit unclear to assume final units of time

Answer :

It is D because you have to subtract 4.73 from both sides in order to isolate the y by itself and get the answer which is 3.27

Step-by-step explanation:

             - - - - - - - -- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -- -

[tex]\blue{\textsf{\textbf{\underline{\underline{Question:-}}}}[/tex]

What is the solution to the equation below?

y+4.73=8.0

[tex]\blue{\textsf{\textbf{\underline{\underline{Answer and how to Solve:-}}}}[/tex]

To solve it, simply subtract 4.73 from both sides:-

y=3.27 (Option D)

         - - - - - -- - - - - - - - - - - - - - - -- - - - - - - - - - - - - - - -- - - - - - - - - - -

Answer:

3/4

Step-by-step explanation:

(36÷12)/(48÷12).

g

Answer:

x+5>11

x>11-5

x>6

So it should be equal to or bigger than 6

Solve for x first

x + 5 = 11

-5

x = 6

So, x is greater or equal to 6 and the symbol next to box is the right one to use.

There should be a shaded in circle at 6, pointing to the right.

( the length of the arrow doesn't matter, you could even extend it to 7, 8, 9 or 10)

Hope this helps!

Answer:

f(n) = 20 + 24n

Step-by-step explanation:

In slope-intercept form, y = mx + b, where m is the slope and b is the y intercept, you need to input the values you are given. f(n) is your "y" here.

The tricky part here is finding "b". Well, at the start, the bamboo shoot is 20 inches tall, so if you think about it, the equation should start with 20, which will be your "b".

Finally, you must show how the bamboo shoot will grow taller by 24 inches each day. Days in this case will be "n", which is like "x" in the general slope-intercept equation, and 24 is your slope ("m"). This will be positive because the height is increasing.

y = 24x + 20 ⇒ f(n) = 20 + 24n

Answer:

Because it starts at 20, that will be your base number

We know it grows 24 in. per day, but we dont know how many, so then we use n

so 20 + 24n

Step-by-step explanation:

20 + 24n

Answer:

v=44

w=68

Step-by-step explanation:

in the diagram above K and I are equal therefore the angles are going to be the same that is why w = 68

for v

since we know two angles out of the three we will equate everything inside the triangle to 180° because that is the sum of angle on a triangle

v+68+68=180( sum of angle in a triangle)

v+136=180

subtract 136 from both sides

v= 44

Answer:

1/9

Step-by-step explanation:

1/3 x 1/3 = 1/9

Answer:

C: strong

Step-by-step explanation:

Its basically asking if the line going through the points fits them. Parabolic would mean the trend line is a parabola, which its not. a parabola is a curved line. weak would mean it doesnt follow most of the points. strong would mean it does follow most of the points, which it does. negative, im guessing would mean it follows none and is completely separate from the points. hope this helps.

Answer:

The accounting equation is a formula that shows the sum of a company’s liabilities and shareholders’ equity are equal to its total assets (Assets = Liabilities + Equity). The clear-cut relationship between a company’s liabilities, assets and equity are the backbone to double-entry bookkeeping. The source of a company’s accounting equation numbers is its balance sheet. Equity can be Shareholders’ Equity, Stockholders’ Equity, or Owner’s Equity.

Like other equations, if two terms of the basic accounting equation are known, you can solve for the third term. For example, Total Assets – Total Liabilities = Total Equity, or Total Assets – Total Equity = Total Liabilities. You move a term from the right side to the left side of the accounting equation by using a minus sign. 

Names meaning the same as Balance Sheet are Statement of Financial Position or Statement of Financial Condition. 

Answer:

29.3

Step-by-step explanation:

its avarage just add everthink and : to 10